Details

sample199.0ms

Algorithm

intervals

Results

85.0ms	84×	body	1280	valid
37.0ms	65×	body	640	valid
35.0ms	258×	body	80	valid
15.0ms	35×	body	320	valid
7.0ms	21×	body	160	valid

simplify192.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	113
7	113
6	101
5	91
4	79
3	70
2	48
1	25
0	12

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l` `sqrt-prod`
32×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
12×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 172

Calls

4 calls:

22.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
29.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
9.0ms	(/ (cos th) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series504.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
155.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
94.0ms	(/ (cos th) (sqrt 2))
85.0ms	(/ (cos th) (sqrt 2))

simplify3.9s

Counts

184 → 184

Iterations

Iter	Nodes
3	7079
2	1764
1	523
0	183

prune728.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b	(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

44×	`times-frac`
43×	`add-sqr-sqrt`
37×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log`
28×	`sqrt-prod`
25×	`associate-l`
14×	`pow1`
12×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`insert-posit16` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`
1×	`associate-*l/`

Counts

4 → 136

Calls

4 calls:

16.0ms	(* (cos th) (* a1 a1))
31.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
46.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
17.0ms	(/ (cos th) (sqrt 2))

series436.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (cos th) (* a1 a1))
140.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
132.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
96.0ms	(/ (cos th) (sqrt 2))

simplify5.1s

Counts

148 → 148

Iterations

Iter	Nodes
3	8393
2	1797
1	530
0	194

prune780.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
345×	`add-sqr-sqrt`
340×	`*-un-lft-identity` `add-cube-cbrt`
37×	`associate-/l*`
25×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
22×	`associate-l`
14×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 473

Calls

4 calls:

44.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
32.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
26.0ms	(/ (cos th) (sqrt (sqrt 2)))
11.0ms	(/ (cos th) (sqrt 2))

series478.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
67.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
151.0ms	(/ (cos th) (sqrt (sqrt 2)))
77.0ms	(/ (cos th) (sqrt 2))

simplify1.2s

Counts

485 → 485

Iterations

Iter	Nodes
2	2931
1	1129
0	480

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.6b	(/ 1 (/ (sqrt (sqrt 2)) (cos th)))
0.6b	(/ (/ 1 (/ (sqrt (sqrt 2)) (cos th))) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

2861×	`times-frac`
1831×	`sqrt-prod`
1332×	`add-sqr-sqrt`
1327×	`*-un-lft-identity` `add-cube-cbrt`
104×	`associate-/l*`
48×	`add-exp-log` `div-inv`
46×	`associate-/r*`
32×	`add-cbrt-cube`
24×	`div-exp`
22×	`associate-l`
12×	`cbrt-undiv`
11×	`associate-/r/`
10×	`pow1`
6×	`prod-exp` `cbrt-unprod`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 1246

Calls

4 calls:

46.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
17.0ms	(/ 1 (/ (sqrt (sqrt 2)) (cos th)))
40.0ms	(/ (/ 1 (/ (sqrt (sqrt 2)) (cos th))) (sqrt (sqrt 2)))
18.0ms	(/ (cos th) (sqrt 2))

series497.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
163.0ms	(/ 1 (/ (sqrt (sqrt 2)) (cos th)))
80.0ms	(/ (/ 1 (/ (sqrt (sqrt 2)) (cos th))) (sqrt (sqrt 2)))
98.0ms	(/ (cos th) (sqrt 2))

simplify32.7s

Counts

1258 → 1258

Iterations

Iter	Nodes
1	3346
0	1248

prune4.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes607.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	20
1	20
0	17

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.7s	2475×	body	1280	valid
1.8s	2117×	body	640	valid
1.3s	8010×	body	80	valid
1.0s	1052×	body	320	valid
625.0ms	540×	body	160	valid